induction
Physics
The generation of an electric current by a varying magnetic field.
Sociology
the derivation of general principles from specific instances
Examples of induction in the following topics:

Inductance
 Specifically in the case of electronics, inductance is the property of a conductor by which a change in current in the conductor creates a voltage in both the conductor itself (selfinductance) and any nearby conductors (mutual inductance).
 Selfinductance, the effect of Faraday's law of induction of a device on itself, also exists.
 where L is the selfinductance of the device.
 Units of selfinductance are henries (H) just as for mutual inductance.
 The inductance L is usually a given quantity.

Inductance
 The answer is yes, and that physical quantity is called inductance.
 Mutual inductance is the effect of Faraday's law of induction for one device upon another, such as the primary coil in transmitting energy to the secondary in a transformer.
 The larger the mutual inductance M, the more effective the coupling.
 Selfinductance, the effect of Faraday's law of induction of a device on itself, also exists.
 where L is the selfinductance of the device.

Logic
 Francis Bacon (15611626) is credited with formalizing inductive reasoning.
 "Bacon did for inductive logic what Aristotle did for the theory of the syllogism.
 Statistical inference is an application of the inductive method.
 While inductive methods are useful, there are pitfalls to avoid.
 Abduction is similar to induction.

Faraday's Law of Induction and Lenz' Law
 This relationship is known as Faraday's law of induction.
 The minus sign in Faraday's law of induction is very important.
 As the change begins, the law says induction opposes and, thus, slows the change.
 This is one aspect of Lenz's law—induction opposes any change in flux.
 Express the Faraday’s law of induction in a form of equation

Proof by Mathematical Induction
 Proving an infinite sequence of statements is necessary for proof by induction, a rigorous form of deductive reasoning.
 The assumption in the inductive step that the statement holds for some $n$, is called the induction hypothesis (or inductive hypothesis).
 To perform the inductive step, one assumes the induction hypothesis and then uses this assumption to prove the statement for $n+1$.
 This completes the induction step.
 Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes.

Sequences of Mathematical Statements
 Sequences of statements are logical, ordered groups of statements that are important for mathematical induction.
 Sequences of statements are necessary for mathematical induction.
 Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers.
 For example, in the context of mathematical induction, a sequence of statements usually involves an algebraic statement into which you can substitute any natural number $(0, 1, 2, 3, ...)$ and the statement should hold true.
 This concept will be expanded on in the following module, which introduces proof by mathematical induction.

Different Lines of Reasoning
 Apply two different lines of reasoning—inductive and deductive—to consciously make sense of observations and reason with the audience.
 One important aspect of inductive reasoning is associative reasoning: seeing or noticing similarity among the different events or objects that you observe.
 Here is a statistical syllogism to illustrate inductive reasoning:
 The conclusion of an inductive argument follows with some degree of probability.
 In order to engage in inductive reasoning, we must observe, see similarities, and make associationsbetween conceptual entities.

Changing Magnetic Flux Produces an Electric Field
 Faraday's law of induction states that changing magnetic field produces an electric field: $\varepsilon = \frac{\partial \Phi_B}{\partial t}$.
 We have studied Faraday's law of induction in previous atoms.
 In a nutshell, the law states that changing magnetic field $(\frac{d \Phi_B}{dt})$ produces an electric field $(\varepsilon)$, Faraday's law of induction is expressed as $\varepsilon = \frac{\partial \Phi_B}{\partial t}$, where $\varepsilon$ is induced EMF and $\Phi_B$ is magnetic flux.
 Therefore, we get an alternative form of the Faraday's law of induction: $\nabla \times \vec E =  \frac{\partial \vec B}{\partial t}$.This is also called a differential form of the Faraday's law.
 Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field.

RL Circuits
 Recall that induction is the process in which an emf is induced by changing magnetic flux.
 Mutual inductance is the effect of Faraday's law of induction for one device upon another, while selfinductance is the the effect of Faraday's law of induction of a device on itself.
 An inductor is a device or circuit component that exhibits selfinductance.
 The characteristic time $\tau$ depends on only two factors, the inductance L and the resistance R.
 The greater the inductance L, the greater it is, which makes sense since a large inductance is very effective in opposing change.

Reasoning and Inference
 Scientists use inductive reasoning to create theories and hypotheses.
 An example of inductive reasoning is, "The sun has risen every morning so far; therefore, the sun rises every morning."
 A faulty example of inductive reasoning is, "I saw two brown cats; therefore, the cats in this neighborhood are brown."
 As you can see, inductive reasoning can lead to erroneous conclusions.
 Can you distinguish between his deductive (general to specific) and inductive (specific to general) reasoning?